Novel Solution for Time-fractional Klein-Gordon Equation with Different Applications

In this paper, for the first time, the Laplace Homotopy Perturbation Method (LHPM), which is the coupling of the Laplace transform and the Homotopy Perturbation Method, is employed to solve non-linear time-fractional Klein-Gordon (TFKG) equations. In other words, for the first time in literature, LHPM is used to solve non-linear TFKG equations. First of all, the procedure of LHPM on TFKG with Caputo fractional derivative is developed. Further, the developed approach of LHPM on TFKG is used for two different examples. This in turn proves the versatile nature of the proposed method. In addition, the validity of the approach is proved by comparing the numerical solutions of both examples with their exact solution. Finally, the comparison of relative errors calculated in each example proves the efficiency and effectiveness of the proposed method on TFKG equations.